Rate Law Calculations

Question

Under certain conditions the decomposition of

carbon dioxide follows a zero order reaction. Given an

initial concentration of 0.333 M and k=0.000234 M/s,

calculate the final concentration in M after 22.2 sec.

Under certain conditions the decomposition of hydrogen

peroxide follows a first order reaction. Given an initial

concentration of 0.251 M and k=0.0000867 𝑠−1, calculate the

final concentration in M after 67.3 sec.

Under certain conditions the decomposition of ammonia follows

a second order reaction. Given an initial concentration of 1.55 M

and k=0.00956 𝑀−1𝑠−1, calculate the final concentration in M

after 91.4 sec.

Answer 1

For a zero order reaction:

[A] = [A]_o - kt

[A] = [0.333 M] - (0.000234 M/s)(22.2 sec)

[A] = 0.333 M - 0.00519 M

[A] = 0.328 M = [CO₂] after 22.2 sec.

For a 1st order reaction:

[A] = [A]_oe^-kt

ln[A] = -kt + ln[A]_o

ln[A] = (-0.0000867 sec^-1)(67.3 sec) + ln[0.251 M)

ln[A] = -0.005835 - 1.382 = -1.376

[A] = 0.253 M = [H₂O₂] after 67.3 sec

For a 2nd order reaction:

1/[A] = 1/[A]_o + kt

1/[A] = 1/[1.55 M] + (0.00956 M^-1sec^-1)(91.4 sec)

1/[A] = 0.645 + 0.874

1/[A] = 1.52

[A] = 0.658 M = [NH₃] after 91.4 sec